Package SubsMat

General:

This module provides a class and a few routines for generating
substitution matrices, similar ot BLOSUM or PAM matrices, but based on
user-provided data.
The class used for these matrices is SeqMat

Matrices are implemented as a dictionary. Each index contains a 2-tuple,
which are the two residue/nucleotide types replaced. The value differs
according to the matrix's purpose: e.g in a log-odds frequency matrix, the
value would be log(Pij/(Pi*Pj)) where:
Pij: frequency of substitution of letter (residue/nucleotide) i by j
Pi, Pj: expected frequencies of i and j, respectively.

Usage:

The following section is laid out in the order by which most people wish
to generate a log-odds matrix. Of course, interim matrices can be
generated and investigated. Most people just want a log-odds matrix,
that's all.

Generating an Accepted Replacement Matrix:

Initially, you should generate an accepted replacement matrix (ARM)
from your data. The values in ARM are the _counted_ number of
replacements according to your data. The data could be a set of pairs
or multiple alignments. So for instance if Alanine was replaced by
Cysteine 10 times, and Cysteine by Alanine 12 times, the corresponding
ARM entries would be:
['A','C']: 10,
['C','A'] 12
As order doesn't matter, user can already provide only one entry:
['A','C']: 22
A SeqMat instance may be initialized with either a full (first
method of counting: 10, 12) or half (the latter method, 22) matrix. A
Full protein alphabet matrix would be of the size 20x20 = 400. A Half
matrix of that alphabet would be 20x20/2 + 20/2 = 210. That is because
same-letter entries don't change. (The matrix diagonal). Given an
alphabet size of N:
Full matrix size:N*N
Half matrix size: N(N+1)/2

If you provide a full matrix, the constructor will create a half-matrix
automatically.
If you provide a half-matrix, make sure of a (low, high) sorted order in
the keys: there should only be
a ('A','C') not a ('C','A').

Internal functions:

Generating the observed frequency matrix (OFM):

Use: OFM = _build_obs_freq_mat(ARM)
The OFM is generated from the ARM, only instead of replacement counts, it
contains replacement frequencies.

Generating an expected frequency matrix (EFM):

Use: EFM = _build_exp_freq_mat(OFM,exp_freq_table)
exp_freq_table: should be a freqTableC instantiation. See freqTable.py for
detailed information. Briefly, the expected frequency table has the
frequencies of appearance for each member of the alphabet

Generating a substitution frequency matrix (SFM):

Generating a log-odds matrix (LOM):

Use: LOM=_build_log_odds_mat(SFM[,logbase=10,factor=10.0,roundit=1])
Accepts an SFM. logbase: base of the logarithm used to generate the
log-odds values. factor: factor used to multiply the log-odds values.
roundit: default - true. Whether to round the values.
Each entry is generated by log(LOM[key])*factor
And rounded if required.

External:

In most cases, users will want to generate a log-odds matrix only, without
explicitly calling the OFM --> EFM --> SFM stages. The function
build_log_odds_matrix does that. User provides an ARM and an expected
frequency table. The function returns the log-odds matrix.

Methods for subtraction, addition and multiplication of matrices:

Generation of an expected frequency table from an observed frequency
matrix.

Calculation of linear correlation coefficient between two matrices.

Calculation of relative entropy is now done using the
_make_relative_entropy method and is stored in the member
self.relative_entropy

Calculation of entropy is now done using the _make_entropy method and
is stored in the member self.entropy.

Jensen-Shannon distance between the distributions from which the
matrices are derived. This is a distance function based on the
distribution's entropies.

_build_log_odds_mat(subs_mat,
logbase=2,
factor=10.0,
round_digit=0,
keep_nd=0)
_build_log_odds_mat(subs_mat,logbase=10,factor=10.0,round_digit=1):
Build a log-odds matrix
logbase=2: base of logarithm used to build (default 2)
factor=10.: a factor by which each matrix entry is multiplied
round_digit: roundoff place after decimal point
keep_nd: if true, keeps the -999 value for non-determined values (for which there
are no substitutions in the frequency substitutions matrix).

_build_log_odds_mat(subs_mat,logbase=10,factor=10.0,round_digit=1):
Build a log-odds matrix
logbase=2: base of logarithm used to build (default 2)
factor=10.: a factor by which each matrix entry is multiplied
round_digit: roundoff place after decimal point
keep_nd: if true, keeps the -999 value for non-determined values (for which there
are no substitutions in the frequency substitutions matrix). If false, plants the
minimum log-odds value of the matrix in entries containing -999